gives the integer closest to x.
rounds to the nearest multiple of a.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- Round rounds numbers of the form x .5 toward the nearest even integer.
- Round[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number.
- For exact numeric quantities, Round internally uses numerical approximations to establish its result. This process can be affected by the setting of the global variable $MaxExtraPrecision.
- Round applies separately to real and imaginary parts of complex numbers.
- Round automatically threads over lists.
Examplesopen allclose all
Basic Examples (3)
Round to the nearest integer:
Round to the nearest multiple of 10:
Plot the function over a subset of the reals:
Numerical Evaluation (7)
Value at two consecutive half-integers:
Complex number inputs:
Single-argument Round always returns an exact result:
The two-argument form tracks the precision of the second argument:
Evaluate efficiently at high precision:
Round threads elementwise over lists:
Round can deal with real‐valued intervals:
Specific Values (6)
Values of Round at fixed points:
Value at 0:
Value at Infinity:
Manipulate Round symbolically:
Find a value of x for which Round[x,2]=2:
Plot the Round function:
Visualize the two-argument form:
Plot Round in three dimensions:
Visualize Round in the complex plane:
Function Properties (3)
Round is defined for all real and complex inputs:
Round can produce infinitely large and small results:
Round is an odd function:
Differentiation and Integration (4)
First derivative with respect to x:
First derivative with respect to a:
Evaluate an integral:
Compute Fibonacci numbers:
Properties & Relations (5)
Negative numbers also round to the nearest integer:
At midpoints, Round rounds towards even integers:
Possible Issues (1)
Round does not automatically resolve the value:
Introduced in 1988
Updated in 1996